4th International Conference on Sensors, Measurement and Intelligent Materials (ICSMIM 2015)
Interaction of Fluid Simulation Based on PhysX Physics Engine
Huibai Wang, Jianfei Wan, Fengquan Zhang
College of Computer, North China University of Technology, Beijing, China
wanghb@ncut.edu.cn, wjf0924@sina.com, fqzhang@ncut.edu.cn
Keywords: fluid simulation, PhysX physics engine, SPH, interaction of fluid and solid
Abstract. To enhance the real-time and interactivity of fluid simulation, a method was proposed based
on smooth particle hydrodynamics(SPH) technique in PhysX physics engine. According to SPH
method, the fluid was treated as a particle system, analyzing composite force of each particle, and
simulating real motion and interaction with static solid and dynamic solid of the fluid on physical
environment. Experimental results show that this method satisfy the requirement of real-time
simulation and the problem of interaction between fluid and solid was also solved.
Introduction
With the study of fluid simulation in recent years, fluid-solid interaction has become a hot research
topic, which is also a difficult problem in computer graphics and virtual reality. It is a complex
technology to simulate the interaction between fluid and solid, because the fluid has no fixed shape, and
the partial differential equation of time and space where the force of motion and interaction is
converted into is extremely difficult to realize in program. Therefore, the sense of reality and
computational efficiency are important criterion in the whole simulation process, however, it is highly
difficult to have these two properties in simulation.
Related Work
The fluid simulation method mainly consists of Euler and Lagrange method. The Euler method is a fluid
simulation method based on grid, but it would consume excessive resources, and easily lead to large
error because of the complex calculation process dealing with large deformation object. Lagrange
method is a method based on particle system, the fluid is treated as lots of particles, and each particle
has its own unique properties, such as position, speed, etc. The Smooth Particle Hydrodynamics(SPH)
is a typical Lagrange method, which is simple and efficient in the simulation process, and is widely used
in various fluid simulation and interaction.
Sun [1] presented a new simulation method for interactions of fluids and deformable solids was. In
this way, both fluids and solids are described by SPH so that avoids complex interface for coupling
fluids and solids. Based on SPH method, a search method by list was proposed, which accelerates
searching the nearest neighbor particles and improves computational efficiency [2]. In order to
simulate the water and water droplets, Kim [3] proposed a regional level sets with a mix of grid and
particle, but this method is difficult to naturally complete the transition of grid and particle. Lenaerts
[4] added number of absorbent particles to each solid particles, simulating the interaction between
permeable materials and water using Darcy's law. Akinci [5] presented a general coupling method
based on solid particle size, which has the characteristics of good reality and high efficiency.
In this paper, we mainly study the simulation method based on smooth particle hydrodynamics
technique in PhysX physics engine, which can maintain the high fluency in the case of large particles.
Introduction of SPH Method
Principle of SPH. Smooth Particle Hydrodynamics is a interpolation method based on fluid dynamics,
which can calculate the physical properties of fluid by interpolation. Navier-Stokes equation, an
important equation describing the motion of incompressible fluid in fluid dynamics, has become the
© 2016. The authors - Published by Atlantis Press
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basic equation in SPH method. This equation describes the conservation of momentum of
incompressible fluid and is equivalent to the Newton's second law. The equation is given as
Du
1
= − ∆p + µ∆2u + f
Dt
ρ
(1)
where ρ denotes the density, u the velocity, μ the viscosity coefficient, f the external force (such as
gravity or force of collision).
In SPH method, every particle carries individual properties. The scalar A(r) at any position r is a
field variable calculated in the Eq. 2:
A(r ) = ∑ m j
i
Aj
ρj
W ( r − r j , h)
(2)
where scalar A(r), which is estimated by a weighted sum of neighboring particles j, can be an arbitrary
property of continuous fluid, such as density, pressure, etc., mj is the mass. The function W(r-rj,h),
called kernel function, is a smoothed kernel with the smoothed radius h which indicates the effective
range of the function. This function is normalized that has the following properties:
∫ W (r − r , h)dr = 1
j
(3)
The left value Du/Dt in Navier-Stokes equation is the acceleration for a given particle. Therefore,
for a given particle, calculating its density and the right values in Navier-Stokes equation firstly, then
calculating resultant force putting on the particle so that the position of the given particle can be
updated according to the kinematic mechanics, this is the principle of SPH.
Basic Idea of SPH. SPH method can be used to solve the partial differential equations of various
energy fields in the fluid dynamics problem. The core idea of SPH algorithm is as follows:
1) The problem domain is represented by a series of arbitrarily distributed particles that do not need
any connection between them.
2) The field function is approximatively indicated by integral method, which is called kernel
approximation.
3) The kernel equation need to be further approximated using kernel approximation method.
4) The given particles depend on particles in current local distribution within each time step.
5) The kernel approximation method is applied to the filed function of all the partial differential
equations in order to obtain a series of discretization of ordinary differential equations which only
relate to time.
6) Explicit integration method is applied to solve the ordinary differential equations in order to
obtain the fastest time integration, and get values of the field variables of all the particles with time.
These six points are combined, which makes SPH algorithm to be a dynamic problem solver with no
grid, adaptive, stable and Lagrange properties.
Fluid Simulation in PhysX Engine
Introduction of PhysX Engine. PhysX engine is one of three major physical computing engine in the
world. It has excellent parallelism and can be carried out quickly on GPU in order to deal with the
integer and floating-point calculation in physical computing. Therefore, PhysX engine can be used to
handle large computational simulation of physical effects, such as fluid dynamics.
In PhysX, all physical motion simulation are completed in a scene, each of which is involved in the
physical computation is actor, and physics is a controller computing and finishing the part of
interactions.
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Fluid Interaction With Static Solid. In the fluid space, particle of fluid enters into the static solid
space, and the reactive force is exerted by the solid which will cause the particle to return to fluid space
needs to be calculated after interaction. The calculation of the force is defined as
F = [k s d + k d (v ⋅ n)]n
(4)
where d denotes the distance of interaction between particle and static solid, Ks and Kd are
respectively the elastic constant and damping constant, v the relative velocity, n the normal vector in
the point of collision, F is the reactive force in the direction of normal vector acting on the fluid particle.
Added the result of dividing the force by mass of particle to the external force term f in Navier-Stokes
equation and the acceleration under this reactive force can be calculated according to the Newton's law
of motion.
Fluid Interaction With Dynamic Solid. The two-way coupling calculation of fluid to solid and
solid to fluid is required when fluid particle reaches the collision distance. The fluid particle produces a
force that causes the solid to move or rotate, simultaneously the solid exerts a reactive force on fluid
particle forcing it to leave the solid.
The process of updating state of solid is described as follows:
1) Obtain the speed in initial state.
2) Solve the forces exerting by each particles.
3) Calculate the external force.
4) Calculate the acceleration of the solid after collision.
5) Update the velocity and position of solid.
Motion Simulation of Fluid. The motion of fluid is followed by Newton's second law which
determines the relationship of mass, acceleration and resultant force of each particles. The force
analysis of fluid particles, including the gravity, the force exerted by external object and the
constraining force between adjacent particles, can be easily divided into the internal force and the
external force. Therefore, the resultant force of the fluid particles is equal to the sum of all force at the
moment t, and we can get
m
∂2S
= Fin ( S , t ) + Fex ( S , t )
∂t 2
(5)
where m denotes the mass of particle, S the displacement vector, Fin is the internal force and Fex is the
external force and both of these two forces are functions of displacement and time changing with t and
S.
In the process of motion, fluid have to be detected collision in each frame so that it can interact with
other objects. Updating motion trajectory of each particles after collision can form the motion effect of
fluid. In PhysX, these collision detection is carried out in each time slice, and the specific detection
process is as follows:
1) Collision filtering. In the scene, all objects involved in physical computing can collide, so it will
cost a lot of time to detect all objects in the case of vast objects. Collision filtering is based on the space
division, only to detect other objects near the current object can save plenty of time and improve the
computing efficiency.
2) Rough collision detection. The fast detection to the collision pairs filtered in step of collision
filtering based on axis-aligned bounding box method is carried out to filter the collision pairs again.
3) Precise collision detection. The precise detection based on triangle is applied to the rest of
collision pairs and the calculation of interaction will be handled if the collision is occurred.
4) End of collision detection.
In the calculation of interaction after collision, the displacement value can be calculated according to
Eq. 5.
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The main steps of fluid motion simulation in PhysX are given by Fig. 1. Firstly, we should initialize
properties of fluid and start the simulation loop. Then the collision detection will be carried out and
calculating resultant force and updating velocity and position of fluid particles and dynamic solid are
executed. Finally render fluid particles and solids and continue the simulation loop.
Fig. 1.
The main steps of fluid motion simulation
Results and Discussions
All experiments in this paper were conducted on a PC with an Intel Xenon E5560 2.13GHz processor,
12GB RAM, and an NVIDIA GeForce GTX 480 graphics card. The version of PhysX 3.3.2 is used.
Table 1: Parameters for experiments
Parameters
Values
Smoothed Radius
0.1
Viscosity
60.0
Dynamic Friction
0.002
Restitution
0.1
Mass of Particles
0.00017269
In the experiments, fluid simulation is carried out under the PhysX physics engine, which can make
the fluid interact with the static solid and the dynamic solid. Some parameters used in the experiments
are shown in Table 1.
The results of interaction between fluid and static solid are shown in Fig.2. When the fluid particles
collide with static solid, the reactive force exerted by solid forces particles to leave, while the solid still
remain in the original state.
Fig. 2. Interaction between fluid and static solid
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The results of interaction between fluid and dynamic solid are shown in Fig.3. When the fluid
particles collide with the dynamic solids, solids are also affected by the fluid particles, which can be
seen from the figures that the stacked blocks are pushed down and the original state is changed.
Fig. 3. Interaction between fluid and dynamic solid
Table 2 shows the relationship between the number of particles and the average frame rate, which
represents the efficiency of the program. As can be seen from Table 2, when the number of particles in
15000, the calculating efficiency is high enough which can satisfy the requirements of real-time
simulation.
Table 2 Numbers of particles and average frame rates
Numbers of Particles
Average Frame Rates
1000
84.35
5000
62.26
10000
38.19
15000
22.81
20000
12.01
Conclusions
We presented a new method for fluid simulation and a experiment based on SPH method is carried out
in PhysX physics engine which simulated a process of interaction between fluid and solids. The result
of experiment showed that the method proposed in this paper can still maintain high frame rate in the
case of a large number of particles which satisfy the requirement of real-time simulation and prove the
feasibility of the method. However, we just performed the simulation using point-based rendering
instead of fluid surface rendering, therefore, we will render the fluid surface using Marching Cubes
method and adding the part of human-computer interaction based on Kinect in order to enhance the
interactivity is taken into account.
Acknowledgements
This research was supported by Project of National Science and Technology Support Plan
(2012BAF84F02).
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